A 2

Scenario

You are working as a research technician at national research laboratory where good analytical skills and understanding of mathematics and Statistical analysis are essential for everyday work within your research group. Your line manager has informed you that to have a successful promotion within your research team during the forthcoming year you need improve and update your present mathematical and Statistical skills so that you can deal with a variety of problems where use of algebraic, trigonometric equations and differentiation and integration on variety of engineering, scientific analysis and calculations are all essential for the new position. In addition, your line manager has also highlighted the importance sound understanding of statistical data collection and analysis that are required to enable you to make positive contributions to your research team in particular with collection, and analysis of the data.
As preparatory task for your forthcoming promotion, your line manager has presented with variety of mathematical and statistical problems and requested from you to present your model solutions to his attention within 2 months to enable him to consider your promotion within the company.LO3: Task 1 (PASS)

1. a) An electronics engineer during a circuit analysis finds 3 currents flowing in different directions and with varied intensities. Each current is represented by a letter and expressed in the form of a vector equation. Let p, q and r be three vector forces, Where p = 4i+ j – 2k, q = 3i – 2j + k and r = i – 2k. Determine the resulting equation of the following expressions (i) (p – 2q) x r (ii) p x (2r x 3q). Briefly give a comment based on your answer.

1. b) A d.c. circuit comprices three closed circuit loops. Applying Kirchoff’s laws to the closed loops gives the following equations for current flow in milliamperes:

Use the Gaussian elimination method to solve for .

1. c) A car is moving along a straight…